When you spend as many years in the classroom as I did, you see lots of innovative ideas come and go; some good and some not so good. I think this is especially true in the field of mathematics. When I first started teaching, the only writing required in high school math courses was the “let x = whatever the variable needs to represent” when doing word problems in algebra and writing the statements and reasons in two-column proofs in geometry. The main emphasis was on being able to crank out right answers, which usually consisted of a combination of numbers and symbols; no words were involved, not even labels on answers. Learning included plenty of memorizing and rote drill and practice. Grading papers meant, for the most part, just checking off answers as right or wrong.
The Evolution of Writing in Mathematics
Over the years, the emphasis shifted to include more of the process rather than just the answer. The math community began to embrace the notion that understanding how and when to apply a particular formula was more important than being able to recite the formula from memory. Learning mathematics came to be much more about developing critical thinking skills than performing calculations and manipulating symbols. We started using open response-type questions to assess deeper understanding of concepts, and the importance of using good writing skills to express that understanding became evident to mathematics educators.
Encourage Math Learners to Write
Students often fail to see past the classroom experience, so it falls to you to convince them of the importance of being able to communicate their understanding of mathematical concepts to others besides yourself. I often heard, “But you know what I meant,” when I insisted that a written explanation was unclear or missing altogether. In fact, I usually did know what the individual meant. In my particular situation, I taught the same group of kids for three consecutive years of high school math and I got to know them and their work quite well. But I wasn’t going to be the one grading their open-response problems on standardized tests, nor was I going to be grading their papers in future college math courses. I tried to get them to realize that anyone who looked at their work should be able to clearly understand their thought process. They often heard me declare, “You have to be able to write exactly what you’re thinking.”
Weave Writing into Your Math Lesson Plans
Incorporating writing into your math curriculum is easier if you take baby steps. You don’t want to overwhelm yourself or the young mathematicians in your charge. Here are some ideas and tips that I found to be effective in my high school math classes. Most can be adapted to different age groups.
- On the first day of class, have pupils write a paragraph or two telling you about themselves. This isn’t an exercise in writing about mathematics, but it’s a good way to convey the idea that writing will be a part of their work in your class. It will give you a quick preview of writing skills while also helping you get to know each member of your class.
- Require a written concluding sentence at the end of all exercises that aren’t drill and practice. For example, if a problem requires finding the number of hours it will take to complete project X, remind your class that they aren’t finished when they solve for a number. Their calculations should be followed by a statement similar to “It will take 5 hours to complete project X.” This shows that the student clearly understands what the result of the calculation represents.
- Insist on clarity. Another favorite reminder I often used was, “Be sure to write precisely what you mean.”
- Use prompts to help you assess the level of understanding of almost any concept. It takes time to read the responses, but the information you gather is usually worth the investment.
- Model good writing in math. Until they get the hang of it, your pupils will probably need to be shown what good writing looks like when used in mathematics. Give them plenty of good examples.
Additional Resources on Writing in Mathematics
A Vocabulary Game
Using the right words is essential when writing about math concepts. This fun game is a good way to ensure that your math writers know and understand key terms, definitions, and properties. Use it for all grade levels.
Independent Study Writing Activities
Designed as independent study exercises to keep fast learners engaged while waiting on others to finish assignments, these ideas can be easily adapted for use by all class members. Activities include writing, editing, and illustrating a math adventure story, creating a book of weird word problems, and researching and creating a lesson plan about ancient number systems.
Logic Puzzles and Critical Thinking
Good readers turn into good writers. Working logic puzzles requires careful reading and analysis to draw conclusions. Use these suggestions about how to develop critical thinking skills by incorporating logic puzzles into your daily routine.